Group theory of Wannier functions providing the basis for a deeper understanding of magnetism and superconductivity

The paper presents the group theory of best localized and symmetry-adapted Wannier functions in a crystal of any given space group G or magnetic group M. Provided that the calculated band structure of the considered material is given and that the symmetry of the Bloch functions at all the points of symmetry in the Brillouin zone is known, the paper details whether or not the Bloch functions of particular energy bands can be unitarily transformed into best localized Wannier functions symmetry-adapted to the space group G, to the magnetic group M, or to a subgroup of G or M. In this context, the paper considers usual as well as spin-dependent Wannier functions, the latter representing the most general definition of Wannier functions. The presented group theory is a review of the theory published by one of the authors in several former papers and is independent of any physical model of magnetism or superconductivity. However, it is suggested to interpret the special symmetry of the best localized Wannier functions in the framework of a nonadiabatic extension of the Heisenberg model, the nonadiabatic Heisenberg model. On the basis of the symmetry of the Wannier functions, this model of strongly correlated localized electrons makes clear predictions whether or not the system can possess superconducting or magnetic eigenstates

Decoherence and single electron charging in an electronic Mach-Zehnder interferometer

We investigate the temperature and voltage dependence of the quantum interference in an electronic Mach-Zehnder interferometer using edge channels in the integer quantum-Hall-regime. The amplitude of the interference fringes is significantly smaller than expected from theory; nevertheless the functional dependence of the visibility on temperature and bias voltage agrees very well with theoretical predictions. Superimposed on the Aharonov-Bohm (AB) oscillations, a conductance oscillation with six times smaller period is observed. The latter depends only on gate voltage and not on the AB-phase, and may be related to single electron charging.Comment: 4 pages, 6 figures, discussion of charging effect change

Interference and Interaction in Multiwall Carbon Nanotubes

We report equilibrium electric resistance R and tunneling spectroscopy dI/dV measurements obtained on single multiwall nanotubes contacted by four metallic Au fingers from above. At low temperature quantum interference phenomena dominate the magnetoresistance. The phase-coherence and elastic-scattering lengths are deduced. Because the latter is of order of the circumference of the nanotubes, transport is quasi-ballistic. This result is supported by a dI/dV spectrum which is in good agreement with the density-of-states (DOS) due to the one-dimensional subbands expected for a perfect single-wall tube. As a function of temperature T the resistance increases on decreasing T and saturates at approx. 1-10 K for all measured nanotubes. R(T) cannot be related to the energy-dependent DOS of graphene but is mainly caused by interaction and interference effects. On a relatively small voltage scale of order 10 meV, a pseudogap is observed in dI/dV which agrees with Luttinger-Liquid theories for nanotubes. Because we have used quantum diffusion based on Fermi-Liquid as well as Luttinger-Liquid theory in trying to understand our results, a large fraction of this paper is devoted to a careful discussion of all our results.Comment: 14 pages (twocolumn), 8 figure

Liquid-induced damping of mechanical feedback effects in single electron tunneling through a suspended carbon nanotube

In single electron tunneling through clean, suspended carbon nanotube devices at low temperature, distinct switching phenomena have regularly been observed. These can be explained via strong interaction of single electron tunneling and vibrational motion of the nanotube. We present measurements on a highly stable nanotube device, subsequently recorded in the vacuum chamber of a dilution refrigerator and immersed in the 3He/4He mixture of a second dilution refrigerator. The switching phenomena are absent when the sample is kept in the viscous liquid, additionally supporting the interpretation of dc-driven vibration. Transport measurements in liquid helium can thus be used for finite bias spectroscopy where otherwise the mechanical effects would dominate the current.Comment: 4 pages, 3 figure

Negative frequency tuning of a carbon nanotube nano-electromechanical resonator

A suspended, doubly clamped single wall carbon nanotube is characterized as driven nano-electromechanical resonator at cryogenic temperatures. Electronically, the carbon nanotube displays small bandgap behaviour with Coulomb blockade oscillations in electron conduction and transparent contacts in hole conduction. We observe the driven mechanical resonance in dc-transport, including multiple higher harmonic responses. The data shows a distinct negative frequency tuning at finite applied gate voltage, enabling us to electrostatically decrease the resonance frequency to 75% of its maximum value. This is consistently explained via electrostatic softening of the mechanical mode.Comment: 4 pages, 4 figures; submitted for the IWEPNM 2013 conference proceeding

Counting Statistics and Dephasing Transition in an Electronic Mach-Zehnder Interferometer

It was recently suggested that a novel type of phase transition may occur in the visibility of electronic Mach-Zehnder Interferometers. Here, we present experimental evidence for the existence of this transition. The transition is induced by strongly non-Gaussian noise that originates from the strong coupling of a quantum point contact to the interferometer. We provide a transparent physical picture of the effect, by exploiting a close analogy to the neutrino-oscillations of particle physics. In addition, our experiment constitutes a probe of the singularity of the elusive full counting statistics of a quantum point contact.Comment: 7 pages, 4 figures (+Supplement 8 pages, 9 figures

Edge Channel Interference Controlled by Landau Level Filling

We study the visibility of Aharonov-Bohm interference in an electronic Mach-Zehnder interferometer (MZI) in the integer quantum Hall regime. The visibility is controlled by the filling factor $\nu$ and is observed only between $\nu \approx 2.0$ and 1.0, with an unexpected maximum near $\nu=1.5$. Three energy scales extracted from the temperature and voltage dependences of the visibility change in a very similar way with the filling factor, indicating that the different aspects of the interference depend sensitively on the local structure of the compressible and incompressible strips forming the quantum Hall edge channels.Comment: 5 pages, 5 figures, final version accepted for publication in Phys. Rev.

Magnetic damping of a carbon nanotube NEMS resonator

A suspended, doubly clamped single wall carbon nanotube is characterized at cryogenic temperatures. We observe specific switching effects in dc-current spectroscopy of the embedded quantum dot. These have been identified previously as nano-electromechanical self-excitation of the system, where positive feedback from single electron tunneling drives mechanical motion. A magnetic field suppresses this effect, by providing an additional damping mechanism. This is modeled by eddy current damping, and confirmed by measuring the resonance quality factor of the rf-driven nano-electromechanical resonator in an increasing magnetic field.Comment: 8 pages, 3 figure